Note that this relation requires \(R_0>1\) .
From the work [1]}, it is known
that under these conditions,
the maximum of \(I(t)\)  in (REF ) can be obtained as
\(\max _{t>0} I(t)= I(0) + S(0) - \frac{1}{b_0 R_0}\ln S(0)- \frac{1}{b_0 R_0}+ \frac{1}{b_0 R_0}\ln \frac{1}{b_0 R_0}.\) 
